The Viola has now lost back-to-back finals.
"Now that 3 days have passed, it still hurts so much and what I say here will make no difference," wrote Martinez Quarta on Instagram.
"But it is the moment to show my face, take our share of the responsibility, get back on our feet and finish the season tomorrow in the best possible way.
"You cannot imagine how much we dreamed of and cared about bringing this trophy to Florence, and how much it hurt not to achieve that.
"Imagining the joy of all the people, the whole city, the whole Viola population: seeing the images of the Stadio Franchi packed, the Viola Park, all the fans who came to Athens to support us, it hurts even more.
"I can only thank all of you and the moment will come to get back on our feet, once again, ALL TOGETHER. I am convinced that sooner or later, it will arrive."